Joan Rivers said Sarah Palin should 'go to another planet and get out of our face'. Photograph: Diane Bondareff/AP

Fox News has cancelled an interview with the comedian Joan Rivers after she described Sarah Palin as "stupid and a threat" and blamed her for the recent attack on an Arizona congresswoman that left six people dead.

The move will reinforce the growing perception that Fox News sees its role as not only to promote Palin but shield her from criticism after the politician – who is also a Fox presenter – was accused of contributing to the extreme political rhetoric that provided the backdrop to the shootings in Tucson.

"I think Sarah Palin is an amazing woman. I think she represents everything strong a woman can be, and I think she should go someplace – to another planet – to show them, and get out of our face," she said.

Rivers was then asked whether Palin should be blamed for the attack in Tucson.

"They're right to blame Sarah for the shootings. Go look at her website. This woman is encouraging sandbaggers to reload ... this woman is just stupid and a threat," she said.

The comedian said that shortly after the TMZ interview, her agent received a call cancelling her appearance on Fox and Friends.

"We got called," Rivers told CNN. "So now we call it Fox and Former Friends. They said to our PR lady it was because of what we said about Miss Palin."

Rivers also tweeted about the incident, saying: "Outcome: DON'T PISS OFF SARAH PALIN. She's apparently 'very powerful', and is obviously still smarting from the end of her reality show."

Fox disputed Rivers' account, claiming that "the volume of news topics" meant there was no room for her on the show.

The topics included a segment on National Penguin Awareness Day, and an assessment of the Aerosmith frontman Steven Tyler's performance as a judge on American Idol.

Fox said Rivers should have been rescheduled but was mistakenly cancelled.